System for analysing the spatial distribution of a function



Jan. 11, 1966 w. TAYLOR SYSTEM FOR ANALYSING THE SPATIAL DISTRIBUTION OFA FUNCTION Original Filed Aug. 28, 1958 5 Sheets-Sheet l F|G.1 12 V ,2 m

I 0 W6 A5 T5 I A e Ej s 2 8 v. 1 1/2 iZATY 1/2 12H! HOW OUTPUT O 500:ZOOV

lNVENTOR WILFRED KENELM TAYLOR ATTORNEY Jan. 11,1966 I w. K. TAYLOR-3,229,236

I y I 7 FIG. 3

5 Sheets-Sheet 5 W. K. TAYLOR Jan. 11, 1966 SYSTEM FOR ANALYSING THESPATIAL DISTRIBUTION OF A FUNCTION Original Filed Aug. 28, 1958 0 n n 0n- O n ooo.oo 0000000 3333 o o o o o o o w w w o o 3 3 3 5 Sheets-Sheet4 W. K. TAYLOR Jan. 11, 1966 SYSTEM FOR ANALYSING THE SPATIALDISTRIBUTION OF A FUNCTION Original Filed Aug. 28, 19 58 Jan. 11, 1966w. K. TAYLOR 3,229,236

SYSTEM FOR ANALYSING THE SPATIAL DISTRIBUTION OF A FUNCTION OriginalFiled Aug. 28, 1958 5 Sheets-Sheet 5 G52) o 0) o 0 do 0 o o o 00 0O COOUTPUT TERM United States Patent 3,22%),2156 SYSTEM FOR ANALYSING THESPATIAL Y DISTRIBUTION 0F A FUNCTEON Wilfred Kenelm Taylor, Chiswiclc,London, England, as-

signor to International Business Machines Corporation, New York, N.Y., acorporation of New York Original application Aug. 28, 1958, Ser. No.757,873. Divided and this application Nov. 13, 1963, Ser. No. 327,573

Claims priority, application Great Britain, Aug. 29, 1957, 27 274 2Claims. ion. ass-77) 'This invention relates to a system for analysingthe spatial distribution of a variable quantity or function.

This application is a division of my copending application, Serial No.757,873, filed on August 28, 1958, and issued on June 1, 1965, as US.Patent No. 3,187,304 which, in turn, is a continuation-in-part of myapplication Serial No. 565,272, filed on February 13, 1956, and issuedon January 9, 1962, as U.S. Patent No. 3,016,518. In U.S.' Patent No.3,016,518 there is-described a system in which signals-derived from aspatial distribution are modi-' fied ins'uch a manner that the largestsignals are obtained from those'zones in the distribution over which thefunction-changes 'inmagnitude' or spatial configuration while smallersignals are obtained from those zones over which the magnitude of thequantity is relatively constant. To this end it was proposed to applythe signals each through an amplifier to a respective output terminal ofa resistance matrix comprising a plurality of pairs of output andfeedback terminals and to apply to the input of each amplifier a signalobtained fromthe respective feedback terminal bycros connecting eachsuch terminal with a selected number of the output terminals of thematrix.

It. is an object of the present invention to provide an improvedarrangement which enables the signals which are derived from those zonesof the distribution where the quantity is relatively constant to be moreeasily eliminated.

A further object of the invention is to provide an arrangement whichavoids the use of feedback and enables undesired signals to beeliminated Without risk of instability.

It is also an object of this invention to provide an improvedorganisation and construction of the resistance matrix whereby itsmanufacture is facilitated.

Other objects and advantages of the present invention will becomeapparent during the course of the following description of Oneembodiment of the invention with reference to the accompanying drawings,in which:

FIGURE 1 is a' diagrammatic representation of the system of thisinvention showing a matrix of light sensitive transducers and a matrixof resistors,

FIGURE 2 is a plan view of part of the transducer matrix of FIGURE '1,FIGURE 3 shows one form of a resistance matrix,

FIGURES 4a-4c and 511-50 shows typical signal patterns obtained by theoperation of the invention,

FIGURES 60-66 illustrate one constructional form of the matrix, and

FIGURE 7 i a wiring diagram of an amplifier.

In the system of the invention signals derived from a spatialdistribution of a variable quantity or function are each applied afteramplification and change of sign or polarity to respective firstterminals, hereafter called transfer terminals, of a resistance matrix,while a fraction of each signal is applied directly to respective secondtennina1s,.hereafter called output terminals, of the matrix, the firstand second terminals being interconnected by resistors in a manner to bedescribed in detail below.

3,229,236 Patented Jan. 11, 1966 nals are arranged in the form of amatrix of equally spaced rows and columns but in general any suitablegeometrical arrangement may be employed. For the purpose of descriptionthe input signals will be taken to be Voltages that are supplied bylight sensitive transducers and it will be assumed that the voltagesupplied to any input terminal is proportional to the integrated lightintensity falling on the transducer situated at a corresponding positionin a matrix of transducers. With this arrangement uniform illuminationof all the transducers will cause equal signal voltages, denoted by i,to appear at all the input terminals of the apparatus, assuming thatthere'is a one to one correspondence between transducers and inputterminals. In general, however, the input signals may be derivedfrom'any suitable sources.

The basic operation of this form of the invention will be described withthe aid of FIGURES 1 to 3. For the sake of clarity only a part of theapparatus is shown in these figures but this includesa complete patternof connections and apparatus-of any size may be constructed l byrepeating the section shown in FIGURE 3 without limit, the. sectionsbeing joined together by connections of the type that are discontinuedin this figure.

Referring firstly to FIGURES 1 and 2, there'is shown a matrix of ninelight sensitive transducers P to P onto which an image'of the letter.T,"for' example, is projected by optical means L. The output of eachlight "sensitive transducer is applied as an input signal to therespective input terminals I to 1,, and is transmitted to the resistancematrix M on the one hand through resistors r, to r, to the outputterminals 0 to O and on the other hand through amplifiers A to A to thetransfer terminals T to T9. I

The input signal voltages supplied to the nine input terminals I I v. I,.will be denoted by i i i and the output signal voltages of theapparatus obtained at the nine output terminals 0 O 0 are denoted by 0 00 It will be observed that a fraction of the voltage i '(n taking allpossible values corresponding to input terminals) is supplied through aresistor of r ohms to the nth output terminal where it contributes to isone form of the system of this invention, the termi- I the outputvoltage o In this form of the apparatus the contribution is equal to i.R/ (R+8i'). The input voltage i is also supplied to an amplifier A ofgain v[G], there being one amplifier for each input terminal. Allamplifiers A to A are similar and multiply the input voltage supplied tothem by [G] and also change its sign or polarity. Thus if an input i isone volt positive and [G] is 2, the output of the amplifier supplied byi is 2 volts. The output of each amplifier is taken to transfer terminalT, shown for convenience in FIGURE 3 as. the outer conductive ring, andwhich is connected through eight equal resistors of R ohms to each ofthe eight nearest output terminals 0 of the matrix. Likewise the outputterminals 0, shown for convenience as inner conductive rings, areconnected through eight resistors of R ohms to each of the eight nearesttransfer terminals T, excluding in this instance the concentric outerring, although in other forms of the apparatus it may be convenient toinclude a ninth resistor between the concentric rings. In FIGURE 3 theeight resistors connected to the transfer terminal T which is suppliedby the amplifier A connected to input terminal I are connected to theeight output terminals numbered 1, 2, 3, 4, 6, 7, 8 and 9 and thispattern is repeated for all outer rings.

The output impedance of each amplifier is made much smaller than R sothat the elfect of loading may be neglected and the contribution to theoutput voltage a, from any one of the eight inputs i (1 n 9, n=5) is .i|G]r/(R+8r). I I

' The elimination of input signals over regions of constant signalamplitude is achieved by choosing appropriate values of lGl, r and R. Inthis example of the apparatus the only condition that has to be met isthat R should be equal to 8|G|r and if is unity this requires r to beone-eighth of R. Apparatus satisfying this condition gives zero outputat all terminals for any size of input signals, providing only that allinput signals are either equal or differ by equal amounts from one inputterminal to the next in each horizontal, vertical or diagonal row of thematrix. This property breaks down at the edge of the matrix but sinceoutputs near the edge can be discarded this is not important.

If all inputs are equal the outputs are zero (except at the edges of thematrix) but if one input anywhere within the matrix increases above therest by any amount +A the corresponding output changes from zero to+A/2. This is not the only change produced, all the eight outputssurrounding this non-zero output alsobecome nonzero but in the oppositesense and by a smaller amount -A/ 16. These negative outputs can beeliminated Whereever they occur by connecting a unidirectionalconductive device such as a rectifier or thermionic diode from each ofthe output terminals to the zero voltage reference point which may betaken as earth potential. If negative outputs are to be prevented, therectifiers are connected between all the output terminals 0 and earth asillustrated at O in FIGURE 3, but the rectifiers must be connected theopposite way round if the input signals are negative and positiveoutputs are to be prevented.

The operation of the invention with a more complex pattern of inputsignals will now be explained with reference to FIGURES 4040 and Sa-Sc.In this case it is assumed that the matrix of light sensitivetransducers consists of forty-nine transducers and that the resistancematrix is correspondingly increased as compared with the arrangement ofFIGURES 1 to 3, the connections of the matrix being, however, the sameas shown in those figures. FIGURES 4a and 5a show a pattern of inputsignal amplitude applied to the input terminals I while FIGURES 4b and5b show the pattern of signal amplitude developed at the output terminal0 under one condition and FIG- URES 4c and 5c show the pattern of signalamplitude developed at the output terminals under another condition.

Referring first to FIGURES 4a-4c, the input pattern shown in FIGURE 4ais formedby adding an amount A to input terminals 17, 18, 19, 25 and 32,this being in addition to a background signal i which is supplied to allinput terminals and which is to be eliminated by the apparatus. It willbe noted that the pattern of signals A correspond to a T of intensity 'i-i-A in a darker background of intensity i The function of the apparatusis firstly to separate the T from its background, thus preventing thebackground signals that do not contain any useful information about thepattern from overloading or otherwise interfering with subsequentapparatus that may be used to analyse the pattern further. Given thesame values of [GI and r used in the last example, the output signalswithout the rectifiers are as shown in FIGURE 4b and with the rectifiersconnected to eliminate negative signals only the positive outputs shownin FIGURE 40 remain. The T is thus isolated from the background but isslightly distorted in intensity, the extremities of the letter givingrise to larger voltages than the central parts. This type of distortionis an advantage in some applications of the apparatus and represents apartial elimination of the central parts that would increase if the Twere increased in size to cover a larger number of light-sensitivetransducers until eventually output signals corresponding to the centralparts of a large T would become zero, leaving non-zero output signalsround the outline of the shape.

The apparatus will also operate correctly when a pattern at the input isdarker than its background as it usually is in printing, the pattern ofa letter of the alphabet printed in dark ink on white or grey papergiving rise to signals of intensity i A and the paper itself giving riseto the background signals i Thus a dark grey T on light grey paper willproduce input signals that are equal everywhere to i except for inputs ii 1' 1' igz which become i A. The inputs and outputs corresponding tothis example are shown in FIGURES 5(1-56 which correspond to FIGURES4a-4c. v

The form of the resistance matrix shown in FIGURE 3 may be constructedin the conventional Way by solder-. ing resistors and amplifiers to theconducting ring terminals but this involves considerable labour if alarge number of input terminals is employed.

An embodiment of the matrix that gives the results already described butwhich is relatively simple from a constructional standpoint wil now bedescribed with the help of FIGURES 6a-6e. A slab of insulating materialS has grooves G formed in the surface to a suitable depth, which inFIGURE 6e can be seen to be half the thickness of the slab. The width ofthe grooves is small compared with the separation of the inputterminals, the positions of which are assumed to be marked out in rowsand columns on the surface of the slab. Grooves are formedalong everyalternate row and along every alternate column of terminal points andfurther grooves are cut at- 45 degrees to the horizontal and verticalgrooves so as to pass through their intersection points. The grooves maybe cut into the insulating slab or they may be obtainedby a mouldingprocess or by any other convenient means. The width and depth of thegrooves may be varied throughout their length and they may be completelysubmerged in the insulating material to form what might be calledtunnels.

The grooves G are filled with a resistive material to form a network ofinterconnected resistors or resistive pathways. A conducting disc D isarranged to make contact with the resistive material in the grooves ateach terminal point. The disc may be evaporated or electricallydeposited on to the block or it may be replaced by a metal plug that isinserted into a hole drilled into the block. Two holes H are drilledthough each disc and through the underlying resistive and insulatingmaterial. As shown, one hole is made larger than the other and theirpositionsare the same in each disc that is not situated at a meetingpoint of a horizontal, vertical and two diagonal grooves. At such pointsthe positions of the larger and smaller holes are interchanged. Fourslabs constructed in this manner are required to construct the form ofmatrix shown in FIGURE 3. Before the four slabs are assembled they aremoved relative to each other until they occupy the positions shown inFIGURE 6e. The edges of the slabs will then be slightly out of line butas already stated the edges of the distribution of signals are not usedand the edges of the slabs may be cut level if desired.

With the four slabs arranged one above the other, as illustrated in theside sectional elevation of FIGURE 6e, conducting wires or rods W arepushed through all the; sets of four holes until they occupy thepositions shown. The wires are a push fit in the smaller holes and somake contact with the discs D wherever a small hole occurs. The diameterof the larger holes in somewhat greater than the diameter of the wiresand no contact is made when a wire passes through a large hole. InFIGURE 6e the wires W on the left of each pair form the transferterminals T and are connected to input terminals I each throughamplifier A and the wires W on the right of each pair are connected tooutput terminals 0. The resistors labelled r in FIGURES l and 3 are seenconnected between the input and output terminals in FIGURE 6e.

The resistance of a groove of length 1, width w and depth d containingmaterial of resistivity p is equal to p wd and it w a d d a e constantthroughout the slab the resistance of all paths between terminals is notthe same, as it is in the arrangement described with reference to FIGURE3 but has the value R =pl/wd for horizontal and vertical paths and thevalue R =p /l/wd for diagonal paths, 1 being the shorter distancebetween neighboring signal points on horizontal or vertical rows andcolumns. It can be shown that the apparatus Will function as requiredwith R greater than R although these resistances could easily be madeequal by increasing the width of vthe diagonal grooves fi? times.Whether R is greater than R by the /E or equal thereto, these resistorsare effectively equal-valued since as above noted the apparatus willfunction as required under either circumstance.

Many variations, elaborations and simplifications of the pattern ofconnectivity given in FIGURE 3 and FIG- URES 6a-6e will give the desiredproperty of converting a set of inputs which are either equal or differby equal amounts from one terminal to the next in horizontal, verticalor diagonal rows, over a large area to zero outputs but the secondproperty whereby small superimposed signals produce outputs is modifiedin general by changes in the pattern of connectivity. The apparatus mayfor example be simplified by omitting all diagonal connections or it maybe made more elaborate by introducing horizontal, vertical and diagonalconnections in excess of those shown so that a given output terminalreceives signals from some or all of the sixteen amplifiers thatsurround the eight amplifiers nearest to the output considered. Thechoice of the number of surrounding amplifier outputs that willcontribute towards the resultant signal at any output terminal dependson the size of the super-imposed input patterns that are of interest inany particular application. As a general guide it can be said that theeight connections to surrounding amplifiers shown in FIG- URES 3 and6a-6e will be suflicient for many applications but that this number maybe increased if large input signal patterns are to be analysed.

A suitable circuit for the amplifiers A, giving the required reversal ofsign or polarity and a gain of unity, is shown in FIGURE 7. It comprisesa double triode valve, the first half of which gives the required gainand change of sign of the input signal voltage, while the second halfacts as a cathode follower to give a low impedance output signal. Thegain is adjusted by means of the variable resistor P2 and the outputvoltage is set to zero when the input is zero by means of the variableresistor P1.

What I claim is:

1. A resistance matrix for use in analysing a plurality of signalsrepresentative of a spatial distribution of a variable quantitycomprising a plurality of sheets of insulating material, each said sheethaving a plurality of electrically conductive terminal portionsregularly arranged in rows and columns and electrically resistive pathsextending between said terminal portions along alternate rows andcolumns and diagonally between the intersection of said paths, means formounting said sheets with said terminal portions in superposedrelationship, and means for connecting certain of the terminal portionsin each superposed set with a first terminal and the other terminalportion of the set with a second terminal.

2. A resistance matrix for use in analysing a plurality of signalsrepresentative of a spatial distribution of a variable quantitycomprising a plurality of sheets of insulating material, each said sheethaving a plurality of electrically conductive terminal portionsregularly arranged in rows and columns and electrically resistive pathsextending between said terminal portions along alternate rows andcolumns and diagonally between the intersection of said paths, means formounting said sheets with said terminal portions in superposedrelationship, and terminal means extending through each superposed setof terminal portions and in electrical contact with certain of saidportions.

References Cited by the Examiner UNITED STATES PATENTS 1,767,715 6/1930Stoekle 338-308 X 2,629,166 2/1953 Marsten et al 338-309 X 2,884,5084/1959 Czipott et a1. 338309 X RICHARD M. WOOD, Primary Examiner.

1. A RESISTANCE MATRIX FOR USE IN ANALYSING A PLURALITY OF SIGNALSREPRESENTATIVE OF A SPATIAL DISTRIBUTION OF A VARIABLE QUANTITYCOMPRISING A PLURALITY OF SHEETS OF INSULATING MATERIAL, EACH SAID SHEETHAVING A PLURALITY OF ELECTRICALLY CONDUCTIVE TERMINAL PORTIONSREGULARLY ARRANGED IN ROWS AND COLUMNS AND ELECTRICALLY RESISTIVE PATHSEXTENDING BETWEEN SAID TERMINAL PORTIONS ALONG ALTERNATE